Apparent migration of tremor source synchronized with the ...gachon.eri.u-tokyo.ac.jp/~hitosi/Projects/Aso2003... · At Aso volcano, Kyushu, Japan, several different types of volcanic

al Research 154 (2006) 181–200www.elsevier.com/locate/jvolgeores

Journal of Volcanology and Geotherm

Apparent migration of tremor source synchronized with the change inthe tremor amplitude observed at Aso volcano, Japan

Noriaki Takagi a,⁎, Satoshi Kaneshima b, Hitoshi Kawakatsu c, Mare Yamamoto d,Yasuaki Sudo e, Takahiro Ohkura e, Shin Yoshikawa e, Takehiko Mori f

a Tokyo Institute of Technology, 1-12-1 Ohokayama Meguroku Tokyo, Japanb University of Kyushu, 6-10-1 Hakozaki Higashi-ku Fukuoka, Japan

c Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi Bunkyo-ku Tokyo, Japand Tohoku University, 6-3 Aoba Aramaki Aoba-ku Sendai-shi, Japan

e Aso Volcanological Laboratory, Kyoto University, 5280 Kawayo tyouyou-mura Aso-gun Kumamoto-ken, Japanf Geological Survey of Japan, 1-1-1 Higashi Tsukuba-shi Ibaraki-ken, Japan

Received 21 December 2004; received in revised form 15 December 2005; accepted 1 February 2006Available online 20 March 2006

Abstract

At Aso volcano, Kyushu, Japan, several different types of volcanic tremor have been observed for many years. One of them isthe continuous tremor, the ground vibration which has dominant frequency between 3 and 10 Hz and has approximately constantamplitudes without any clear beginning and ending. We observed the continuous tremor at Aso using short period seismometerarrays for 3 days in 1999. We locate the source of the continuous tremor by seismic array data processing. We use the semblancecoefficients in order to estimate the arrival azimuth and apparent slowness by grid search. The epicenters of the continuous tremorare located around the currently active crater, and the source depths are likely to be shallower than 600 m. We find that theestimated epicenter clearly migrates synchronized with the change in the tremor amplitude. The migration often occurs periodicallywith a period of about 80 s, but aperiodic occurrence of the migration is also often seen. In both cases, the epicenter is locatedsoutheastward (northwestward) when the amplitude is larger (smaller). We propose that there are two or more independent tremorsources with fixed locations, and that their amplitudes modulate either aperiodically or periodically with periods nearly 80 s. Thetremor signals from those sources are mixed at the arrays, and the estimated epicenter parameters vary according to which signaldominates the seismograms. The simplest model is that there are two point sources, one at west and the other at south of the crater(we call the two sources as “NW source” and “SE source”, respectively), and the amplitude of the SE source changes with time.Consequently, the SE source dominates the seismogram when the observed amplitude is larger, whereas the NW source dominateswhen the amplitude is smaller. We generate synthetic seismograms, and apply the location technique to them to verify the validityof the two point source model and to search the locations of two sources which can explain the observed synchronization betweenthe amplitude and the apparent epicenter location. We find that the distance between the two sources needs to be more than 400 mto agree with the observation. We also analyze the seismic array data observed in 2001, and infer that the NW source in 1999 maybe identical to the tremor source of the 2001 data.© 2006 Elsevier B.V. All rights reserved.

Keywords: volcanic tremor; tremor; array; semblance; amplitude modulation

⁎ Corresponding author. Fax: +81 3 5734 3538.E-mail address: [email protected] (N. Takagi).

0377-0273/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.jvolgeores.2006.02.001

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182 N. Takagi et al. / Journal of Volcanology and Geothermal Research 154 (2006) 181–200

1. Introduction

1.1. Volcanic tremor and locating its sources

Excitation of volcanic tremor is one of the mostimportant seismic phenomena at active volcanoes.Observations of volcanic tremor are practically impor-tant because they can be utilized in eruption warning andvolcanic hazard mitigation. From a purely scientificpoint of view, on the other hand, volcanic tremors areoften conceived to represent fluid motion in the edificeof volcanoes. For that purpose, volcanic tremors havebeen observed at many active volcanoes around theworld. Their characteristics vary from volcano tovolcano or change with time even for one volcano.Chouet (1996) classified seismic activities at volcanoesinto VT and LP seismicity. A VT (volcano-tectonicearthquake) is a shear faulting in solid rock, which is thesame process as a tectonic earthquake. On the otherhand, LP seismicity is considered to originate inpressure fluctuations of the fluid surrounded by solidrocks, and includes LP events and tremor. LP eventshave a typical period of 0.2–2 s with durations of fewtens of seconds. On the other hand a tremor is asustained oscillation whose duration ranges fromminutes to days, or even longer on some occasions.LP events and tremors have similar spectra, slownesses,and source locations at many volcanoes such as Kilauea(Almendros et al., 2001), and Montserrat (Neuberg etal., 2000).

The source location of a volcanic tremor is one of themost important pieces of information. But it is usuallydifficult to accurately locate a tremor source because Pand S waves cannot be distinguished clearly on thetremor seismograms, and wave forms often significantlyvary from receiver to receiver due to large site and patheffects for volcano edifices. These difficulties could beovercome to some extent by deploying dense seismicarrays. Recent developments in seismometry haveenabled us to discriminate difference in the phase ofseismic waves from receiver to receiver, which can beconverted to the time lag. We therefore can estimateapparent slowness (which is inverse of apparentvelocity) and back azimuth of tremor signals withreasonable accuracy by using seismic array technique.There are several different kinds of methods fordetermining apparent velocities of seismic wave fieldsfor locating the wave source. The frequency domainmethods include the f–k spectrum method (Lacoss et al.,1969), the cross spectrum method (Ito, 1985), and theMUSIC technique (Goldstein and Archuleta, 1987;Goldstein and Chouet, 1994; Chouet et al., 1997;

Almendros et al., 2001; Saccorotti et al., 2004). On theother hand, the time domain methods for locatingsources of volcano-seismic signals utilize, for instance,the cross correlation function (Almendros et al., 1999;Ibanez et al., 2000), or the semblance coefficient (Neideland Taner, 1971; Kawakatsu et al., 2000). In this studywe use semblance-based techniques in order to locatethe source of the continuous tremor at Aso volcano, inKyushu, Japan.

1.2. Volcanic activity at the Aso volcano

The Aso volcano is one of the most prominent activevolcanoes in Japan (Fig. 1). There are 7 craters at theNaka-dake summit, the first of which currently emitsvolcanic gases (star in Fig. 1). We call this crater as themain crater. The last magmatic eruption occurred from1989 to 1991 at this crater. Except for the gas emission,there was no significant volcanic activity at the surfaceduring the observations in 1999. Although such a quietstage of volcanic activity has continued for more than10 years at Aso, volcanic tremors have always beenobserved. The volcanic tremors at Aso have beenhistorically classified according to their dominantperiods by Sassa (1935). By updating his classification,we classify seismic signals of volcanic origin at Aso asfollows:

Type a) Long period events with the period of 15 s.Type b) High frequency (shorter period) tremor with

dominant frequency around 3 to 10 Hz, whichoccurs continuously. We call this type oftremor as “continuous tremor”, or simply as“tremor”.

Type c) An isolated events with dominant frequencyaround 1 to 2 Hz.

The source of the Type a events is located accuratelyat depths of 1 to 1.5 km about 400 m south-west of themain crater (Kaneshima et al., 1996; Legrand et al.,2000; Kawakatsu et al., 2000). The kinematic descrip-tion of the source mechanism of the Type a events is acombination of isotropic expansion/contraction and aninflation/deflation of an inclined tensile crack (Kane-shima et al., 1996; Yamamoto et al., 1999; Legrand et al.,2000). As for the higher frequency signals (Type b or c),Kikuchi (1963) proposed that the tremor of 2–5 Hzconsists of surface waves produced by small volcanicearthquakes. Signals of the Type c events continue nearly20 s and are sometimes preceded by an even higherfrequency volcanic signals of 10 Hz (Mori, 2000). More-over the Type c events occur almost simultaneously with

Fig. 1. (Top) Location of Mt. Aso (inset) and a topography map of the Aso volcano. Star marks the center of the Naka-dake main crater. Solid dotsshow the locations of the sensors of the 1999 arrays (dark) and the 2001 array (light), respectively. Contour interval of the topograph is 15 m. (Bottom)Enlarged maps of the arrays.

183N. Takagi et al. / Journal of Volcanology and Geothermal Research 154 (2006) 181–200


the Type a events (e.g., Kaneshima et al., 1996). Mori(2000) investigates some events of Type c and concludesthat the sources are located at southeast of the maincrater, at a depth of about 600 m. Yamamoto (2004)analyzes the Type c events, and concludes that the sourcemechanism mainly consists of a radial motion of thesidewall of a nearly vertical cylinder.

Based on the preliminary results from the arrayanalyses of the continuous tremor (Type b) that it has alarger apparent slowness than the Type c events, Takagi(2002) concludes that the source of the Type b tremor isshallower than that of Type c events. Another notableobservation of the continuous tremor (Type b) is thatduring the observation in November 1999, its amplitude

Fig. 2. Examples of the vertical component velocity seismograms observed atspectrogram. The horizontal axis represents time in seconds. The vertical axisshown with gray scale. An amplitude modulation with a period of 80 s can becomponent observed during the 1999 observation at the west array for 10 min(Bottom) Seismogram and spectrogram observed at the sensor 00 of the nor

modulated either periodically or aperiodically. This is arather rare phenomenon for the Aso volcano, whoseoccurrence continued only a few months. In this study weinvestigate the relationship between the modulation andthe source location. The results offer some valuable hintsto understand the mechanism of the continuous tremor atthe volcano in a quiet stage.

2. Observation

2.1. The 1999 observation

For three days in November, 1999, two seismometerarrays were deployed near the Naka-dake main crater by

the center (sensor 00) of the west array during the 1999 observation andof the spectrogram is frequency from 0 to 15 Hz. The power spectra areseen. (Top) An example of seismogram and spectrogram for the verticalfrom 22:00 to 22:10, on Nov. 26, 1999. The sensor is at the array center.th array during the same period as the top panel.


a joint team of Tokyo Institute of Technology,University of Tokyo, and University of Kyoto in orderto observe volcanic tremors. As shown in Fig. 1, thearrays were installed at west and north of the maincrater, nearly 700 m from the center of the crater lake.Hereafter we call these arrays ‘the west array’ and ‘thenorth array’, respectively. Each array consisted of29 seismographs with a semi-circular form. The aperturelengths of the west and north arrays were 160 and200 m, respectively. At stations 00, 14, 24, 34, 44, 54,64, and 74 which were located at the outer rim of thesemi-circular arrays, three component velocity seism-ometers with a free period of 1 s (Lennartz LE-3D) wereinstalled, while at other stations vertical componentvelocity seismometers with a free period of 0.5 s (MarkProducts, L22D) were installed. Seismic signals weredigitized with 16 bits and stored in data loggers with a20 M bytes static memory (LS-8000SH, HAKUSAN).The sampling rate was 0.01 s, and the internal clocks ofthe data loggers were corrected with GPS signals onceevery hour giving high enough accuracy of timing. Theobservations were performed for three nights (33 h). Thelocations of the stations were determined by the GPS

Fig. 3. (Top) The vertical component velocity seismograms observed at selecteFig. 2 is shown. See Fig. 1 for the sensor locations. The seismograms are domof signals are seen across the array. (Bottom) Examples for the vertical cobservation for the same time window as above.

quick static location technique, with high enoughaccuracy (on the order of 10 cm) of the relative locationsof the stations.

2.2. Characteristic features of the data

Figs. 2 and 3 show examples of the spectrograms andseismograms, respectively. During the 1999 observa-tion, many Type c events were recorded. We can seeisolated events (Type c) in Fig. 2 at about 100, 120, 150,310, and 325 s. Most of the isolated events last for 10 to20 s. The continuous tremor lasts at least for severalyears, and it is seen throughout the time window in Fig.2. The dominant frequency band of the continuoustremor (Type b) is from 3 to 10 Hz. The particle motionof the tremor is complicated. At the west array, themotion in the direction transverse to the center of thecrater lake (called ‘transverse’) is dominant. On theother hand, the direction of the dominant motion scattersamong the sensors at the north array.

The amplitude of the continuous tremor during the1999 observation sometimes modulated periodically.Such a periodic amplitude modulation of the continuous

d sensors of the west array during the 1999 observation. The first 5 s ofinated by the continuous tremor for this time window. Coherent arrivalsomponent seismograms observed at the north array during the 1999


tremor seems a rather rare phenomenon at Aso, althoughit lasted for a few months in late 1999. During the 1999observation, the period of the modulations was about80 s (Fig. 2). To quantify this phenomenon we calculatemoving averages of the absolute value of the amplitudeat sensor 00 of the west array over a time window of10 s, obtaining a time series of smoothed absolute valueswith a time interval of 1 s. We then compute auto-correlation coefficients of the smoothed absolute valuesfor each hour of the observation. The result is shown inFig. 4. The periodic amplitude modulation appearsintermittently during three days of the 1999 observation.Even when such periodic amplitude modulating is notseen, the tremor amplitudes change with time. We callthese ‘aperiodic amplitude modulations’.

3. Method of searching tremor source parameters

3.1. Grid search method with semblance coefficient

In this study, we estimate two parameters, θ and s,which represent the azimuth of the epicenter from thearray and the apparent slowness of seismic waves,respectively. The seismic signals are regarded as planewaves propagating horizontally so that the hypocentraldepth is not determined. The velocity structure isassumed to be homogeneous. We also take anassumption that the sensors are on the same horizontalplane although the maximum difference in the heightamong the sensors amounts to 20 m for the west array ofthe 1999 experiment. We use the semblance coefficient(Neidel and Taner, 1971), S, in our seismic arrayanalyses. The time series of signal at the n-th sensor is

Fig. 4. Auto-correlation functions of the 10 s moving averages of the absolutewest array. We use the first 600 s of the data in every hour. The horizontcoefficient, respectively. (Left) Examples for the time windows which showtime of about 80 s. (Right) Examples for the time windows which show aperiseen, the amplitudes do change with time.

indicated as un(tm) where tm is the m-th time step, whilethe time lag of the wave for the n-th sensor is written asτn:

sn ¼ −sðXncoshþ YnsinhÞ ð1Þ

where Xn and Yn are the cartesian coordinates of the n-thsensor relative to the center of the array, and θ is theback azimuth of the incident wave measured counter-clockwise from the east. The x and y axes correspond toeast and north, respectively. The total number of sensoris N (=29). The number of the data points contained inthe time window and the sampling interval areM and Δ,respectively. Therefore tm is written as tm=mΔ. The timewindow to be used for the n-th sensor starts fromtm0

=m0Δ+τn, and ends at tm0+M=(m0+M)Δ+τn. Thenthe semblance coefficient is defined as follows,

S ¼Pm0þM

m¼m0

PNn¼1 unðtm þ snÞ

n o2

NPm0þM

m¼m0

PNn¼1 unðtm þ snÞ2

ð2Þ

The value of S depends on τn. When signals arecoherent and τn is chosen to match the time lag of anactual wave field for each sensor, S takes themaximum. The value of τn is calculated for eachsensor for a given parameter set (θ, s). When θ and sare in agreement with the true values, S should takethe maximum.

The obtained semblance coefficients for differenttime windows usually show substantial scatters, sug-gesting the necessity of some sort of smoothing. Wesuppose that there are J time windows. After wecalculate the semblance coefficients Sj(θ, s) for each of

value of the amplitudes observed on Nov. 26, 1999 at sensor 00 of theal and vertical axes represent lag time (second) and auto-correlationperiodic amplitude modulations. Most of them show a peak at the lagodic modulations. Although no periodic change in amplitude is clearly


these data windows (j=1,2,…,J), we estimate theparameters θ and s by averaging these semblancecoefficient over the J windows.

S ðh; sÞ ¼1J

XJj¼1

Sjðh; sÞ ð3Þ

The parameter set (θ, s) for which the averagedsemblance S (θ, s) takes the maximum value is regardedas the most probable estimate of the parameter set. Basedon our preliminary analysis, we set the searching rangeof azimuth and apparent slowness as − 10° to 50° and 0.6to 1.5 s/km for the west array, −80° to −50° and 0.4 to1.0 for the north array. In this study azimuth is measuredcounterclockwise from east, so that azimuths 0° and 90°correspond to east and north, respectively. For the gridsearch, we use grid intervals of 0.02 s/km and 0.2° forapparent slowness and azimuth, respectively. In theactual analyses, we calculate semblance coefficients for0.5 s time windows (called ‘short window’). There is nooverlapping between two adjacent short windows. Wethus obtain 41 short windows from a record which is20.5 s long. We call such a 20.5 s window as a ‘longwindow’. For each long window we average thesemblance coefficients for each parameter set over the41 short windows in it. We then obtain one set ofparameters, (θ, ŝ) which gives the maximum averagedsemblance, S , for the long window. The process isrepeated for the next long window which is shifted by 1 sfrom the previous one. Finally we obtain a time series ofthe parameter set with 1 s intervals.

3.2. Estimation of epicentral region using two arrays

We can constrain the tremor epicenter reasonablywell because of the presence of two arrays operated atthe same time and because the arrival azimuths of thesignal at the two arrays are well constrained. The detailsof the method to estimate the epicenter region are asfollows; for each long time window we obtain two fan-shaped areas centered at the west and north arrays bytaking the regions within the estimated error bounds ofthe azimuth deduced by the error estimation methodsdescribed below. We consider the area where the twofan-shaped areas overlap as the epicentral area. Forexample, for the data of 3000 s, 2980 of such theepicentral areas are obtained. Next, we divide the regionaround the main crater into grids of 10 m by 10 m. Foreach grid we count the number of long time windowswhose epicentral areas include the grid. We regardthe distribution of the number around the crater as

representing the apparent epicentral area of the contin-uous tremor.

3.3. Synthetic tests for error assessment

3.3.1. Synthetic signals and noisesIn this section, we use synthetic seismograms

which consist of a tremor signal and two differenttypes of noise in order to evaluate errors and biases inthe tremor parameters. To generate a syntheticseismogram, we create random time series with awhite spectrum and apply a band pass filter from 2.0to 8.0 Hz, which corresponds to the dominantfrequency band observed at the two arrays. Thefiltered signals are used for the synthetic tremorsignals and the noises. Tremor signals propagate froma point source as spherical waves with the speed of1.0 km/s and are recorded at the imaginary sensorswhich have the coordinates of the actual sensors (Fig.1). We consider two types of noises, coherent noiseand random noise. The coherent noise representsscattered waves which would originate from hetero-geneous structure in the volcano edifice. In oursynthetic test, they are considered to be plane wavesarriving at the imaginary array from randomlysampled directions. The duration of each packet ofthe coherent noise is 0.5 s, and its velocity is the sameas that of the tremor signal. The packets arrive at thearray with the intervals which also are randomlysampled with the average of 0.5 s. On the other hand,the random noise is included to represent seismicnoise associated with velocity structure beneath eachseismometer. It has no coherency between any of thetwo imaginary sensors.

3.3.2. Evaluation of biases due to the plane waveassumption

The plane wave assumption causes a bias in ourestimation of the azimuth θ. The closer the source is tothe array, the larger is the azimuthal bias. From ourpreliminary analyses, the tremor sources could beregarded as at least 400 m distant from the west array,and 600 m from the north array. We evaluate the biaswhich depends both on the source azimuth and thedistance using synthetic data without noise. Forexample, in the case of the west array, the estimatedazimuth of a source which has the true azimuth of 20°ranges from 20° (for source distances of a fewkilometers) to 24° (for distances of 400 m). In short,the azimuth for the west array tend to be overestimatedby up to 4°. We calculate the range of bias for eachsource azimuth using the synthetic test, and expand


properly the estimated error ranges evaluated by the twomethods mentioned below.

In addition to the plane wave assumption effect, thecoherent noise affects the estimation of apparentslowness. Because of the presence of the coherentnoise signals which arrive at the array from azimuthsopposite to that of the tremor, the apparent slownesstends to be underestimated by up to 0.05 s/km. Weexpand the estimated error ranges for the apparentslowness evaluated by the two methods mentionedbelow.

3.3.3. Two methods of error assessmentWe examine two methods for the evaluation of errors

or uncertainties in the estimated parameters, θ and s.The first method is the one using threshold ofsemblance relative to the maximum semblance (Ohmi-nato et al., 1998; Almendros and Chouet, 2003). Asmentioned in Section 3.1, each long window contains41 short windows, and we obtain the averagedsemblance S (θ, s) by averaging Sj over j for each pairof θ and s. We define Ŝ as the maximum value of S (θ, s),and P(0≤P≤1) as the threshold of relative semblancefor defining the error range. We obtain the range of theparameter set (θ, s) for which S (θ, s) takes a valueexceeding P×Ŝ, and after the correction of the biasesmentioned above define it as the error range. Theparameter set (θ, ŝ) which gives Ŝ is regarded as themost probable parameter set.

The value of the threshold P is chosen based on asynthetic test as follows. In this test the tremor signalswith amplitude of 1.0 (of an arbitrary unit) and a speedof 1.0 km/s are radiated from an imaginary surfacesource which is located at the center of the main crater.Synthetic seismograms are computed for imaginaryseismic receivers at the locations of the actual sensors ofthe 1999 west array. We compute 12 sets of theseismograms. Six of the 12 sets contain random noisewhose amplitude is either 0.2, 0.33, 0.5, 1.0, 2.0, or 3.0,but do not contain coherent noise. The other 6 setscontain no random noise but contain coherent noise withamplitude of either 0.2, 0.33, 0.5, 1.0, 2.0, or 3.0. Thelength of each seismogram is 1021 s. There are 1000long windows for each seismogram, and each longwindow has overlapping of 19.5 s with the two adjacentwindows. We estimate the parameters for the syntheticdata, obtaining 1000 sets of parameters and error rangesfor each of the 12 sets of the seismograms. For variousvalues of the semblance threshold P, we calculate thepercentages of the number of long windows for whichthe true parameters fall inside the error range. When weset P to 0.996, the true parameters fall within the error

range for more than 69% (one sigma) of the timewindows for all of the 12 sets of seismograms. Wetherefore choose 0.996 as the value of P.

The second method for error evaluation usesbootstrap (Efron and Tibshirani, 1993). There are 41short windows (0.5 s long) in a long window (20.5 slong). For each short window included in the longwindow, we calculate the semblance coefficients, Sj(θ, s)(j=1,2,…, 41) for the given ranges of θ and s. We call thegroup of these 41 samples of semblance coefficients as afunction of θ and s, as the original set of semblance, orsimply as “the original set”. We obtain an original set ofsemblance from a long window. Then we take asemblance Sj(θ, s) from the original set 41 times withreplacement, and make another set named as a bootstrapresample set of semblance. Each bootstrap resample settherefore consists of 41 samples of Sj (Sj(l)(θ, s): l=1,2,…, 41: j(l) is a number which is randomly picked up froma set of numbers {1, 2, 3,…, 41}). We repeat theprocedure K times obtaining K bootstrap resample setsof semblance. The k-th resample set is represented asSj(l)k (l=1,2,…, 41) (k=1,2,…,K), where k represents

the number of bootstrap resample. For each pair of θand s, we average Sj(l)

k over l as mentioned in Section3.1, and estimate the most probable parameter set forthe k-th bootstrap set, (θk, ŝk) (k=1,2,3,…, K), for eachlong window. We set K to 50 in this study. For thetwo parameters, we calculate the averages (θ, s ) andthe standard deviation (σθ, and σs) over k. We regardθ and s as the estimates of the parameters, and θ+σθ

(θ−σθ) and s +σs (s −σs) as the upper (lower) boundsof the error ranges. We perform the same synthetic testas for the first method, and confirm that the trueparameters are within the error ranges for more than69% (one sigma) of the long windows. Examples ofthe estimated parameters and error ranges estimated bythe two methods are shown in Fig. 5. In this study weadopt the first method using the semblance threshold,because it gives more conservative estimates for theerror ranges than the bootstrap method. The bounds ofthe error ranges of azimuth and apparent slowness arecorrected for the biases.

4. Analysis of the 1999 data

4.1. Amplitude modulation and migration of epicenter

Figs. 6 and 7 show the results obtained from the dataof the west array and the north array, respectively. Theapparent azimuth and the amplitude of the epicenter ofthe continuous tremor clearly change with time. Theirchanges often synchronize quite well (second row of

Fig. 5. Source parameters estimated from the synthetic seismograms for the 1999 west array. (Top) Synthetic vertical seismogram for a 200 s timewindow. (Second row) Azimuth of the epicenter from the center of the array measured counterclockwise from east. The azimuths of 0° and 90°correspond to east and north, respectively. Solid line shows the estimated parameters, and gray lines show the error ranges evaluated by the methodusing semblance threshold (left) and bootstrap (right). Because the estimated azimuth tends to be overestimated due to the plane wave assumption, theerror ranges are asymmetric about the estimated values. (Third row) Apparent slowness in seconds per kilometer. Details are the same as the secondrow. Because the estimated slowness tends to be underestimated due to the coherent noise, the error ranges are asymmetric about the estimated values.(Bottom) Semblance coefficients. The true values of azimuth and apparent slowness are 27° and 1.0 s/km, respectively.


Fig. 6). This synchronization is more evident for thewest array, but it is seen also for the north array(Fig. 7a). On the other hand, the apparent slownessand semblance values do not synchronize with theamplitudes as clearly as the azimuth (third andbottom rows of Figs. 6 and 7). As a result of thesynchronization between the azimuth and amplitude,

the apparent epicenter tends to be located southeast-ward when the amplitude is large, while it migratesnorthwestward when the amplitude is small (Fig. 6second row), resulting in an epicentral area extendingNW to SE. We plot the number of time windowsdescribed in details in Section 3.2 on the map withgray scale (Fig. 8). Another noticeable observation is


that the amplitude of the continuous tremor modulatessometimes periodically with a period of about 80 s(Fig. 4). Figs. 6a and 7a show the time windows whichcorrespond to periodic modulation, while Figs. 6b and7b are for aperiodic modulation.

There are two possibilities to explain the synchroni-zation between the changes in tremor amplitude andepicentral azimuth. One is that the source of the tremoractually moves to-and-fro synchronized with the

Fig. 6. Examples of the estimated parameters for the west array data plottedperiodic amplitude modulation (a) and aperiodic modulation (b) are shown. V(in degree, measured counterclockwise from east) (second row), apparent slo(bottom row). The azimuth of the main crater is 2°. The estimated parametereach panel, the RMS of the amplitude is superimposed with light gray line. Thby 1 s. The solid arrows correspond to the duration used to be matched with

modulation in its amplitude. The other is that there aretwo or more tremor signals from different sources withfixed locations, and the amplitudes of the tremor signalsmodulate on some occasions with a period near 80 s buton the other occasions aperiodically. The estimatedsource parameters vary according to which of the tremorsignals dominate on the seismograms. The latter modelseems much more plausible, since in the former modelthe tremor sources must migrate more than 300 m within

against time (in seconds). Examples for the time windows which showelocity seismogram of vertical component at station 00 (top), azimuthwness in seconds per kilometer (third row), and semblance coefficients are plotted by thick solid lines with error bounds (thin solid lines). Ine RMS amplitudes are calculated over a time windows of 20.5 s shiftedthe synthetic data in Section 4.2.

Fig. 6 (continued ).


80 s when a periodic modulation occurs, requiring amigration speed more than 3 m/s. In this study weassume for simplicity that there are two sources and thesignal amplitudes of only one of the sources modulate.

We note here that simple applications of semblancemethod, of f–k spectrum, or of MUSIC (Goldstein andArchuleta, 1987; Goldstein and Chouet, 1994; Chouet etal., 1997; Almendros et al., 2001; Saccorotti et al., 2004)to the modulated data, do not resolve two or moreseparated signals. This is confirmed by applying thesemethods to synthetic data which are computed for themodels with two sources. We infer that the aperture ofthe 1999 west array is too small for resolving the twosources. The amplitude modulation does provide us witha chance to infer the presence of two or more sources,

and we describe another method to estimate the twosource locations in the next section.

4.2. Estimation of the two source locations

In this section we estimate the locations of the twosources by performing a synthetic data analysis. In thefirst step we analyze synthetic signals for two tremorsources with a variety of locations around the maincrater, and locate “single source” epicenter, or “apparentepicenter” by assuming that there is only one tremorsource as we did for the real data. The estimatedapparent epicenter depends on the amplitude ratiobetween the two sources, and tends to be locatedbetween the two sources, on a line connecting the two


sources. In our analyses of the 1999 data, the apparentepicenters seem to be distributed along a line strikingNW–SE. This suggests that the two sources arelocated on the line around which the apparent sourceregions are observed (Fig. 8). Fig. 9a shows thelocations (called 0 to 10) of the two sources tested inthe second step of the synthetic analysis. The depthsof the imaginary sources are at the surface of the maincrater lake. One of the two imaginary sources is called“NW source” considering that this is located north-west of the other source, and the other is called “SEsource”.

The apparent epicenters are affected by the twosource locations and the amplitudes of the signals andnoises. We test many patterns of the synthetic

Fig. 7. The estimated location parameters for the 1999 north array for the samcounterclockwise from east is negative for this array, and the azimuth of the

seismograms which have different source locationsand different amplitudes of signals and noises, andexamine how well the estimated parameters match theobservations. For the synthetic data, we define A, B, andR as the RMS amplitudes of the tremor signals from theNW source, the tremor signals for the SE source, and theamplitudes of random noise, respectively. A and Bsatisfy the equations,

B ¼ B1 þ B2 1þ cos −kþ 2ktT

� ��

Aþ B1 þ B2 ¼ 10ð4Þ

where T is the period of modulation, T=80 (s). Thesource locations of the NW and SE sources are

e time windows as that of Fig. 6a and b. Note that azimuth measuredmain crater is −63°. Other details are the same as those of Fig. 6.

Fig. 7 (continued).


represented by the source number shown in Fig. 9a,and defined as LNW and LSE, respectively. In thefollowing analysis, we neglect coherent noise forsimplicity. We use the seismograms of the westarray with duration of 100 s from 22:07:30 on Nov.26 (Fig. 6a) as the observed data to be matched.The duration of each synthetic seismogram is 110 s.The maxima and minima of the parameters whichare obtained by the averaged semblance method(Section 3.1) are computed for the observed seis-mograms (θ obs

max, θ obsmin, a obs

max, a obsmin) and for the

synthetic seismogram (θ synmax, θ syn

min, a synmax a syn

min). Themodel parameters are A, B1, B2, R, LNW, and LSE.The tested ranges of model parameters are shown inTable 1.

We introduce three penalty coefficients; azimuthalpenalty coefficient pθ, amplitude penalty coefficient pa,and semblance penalty coefficient ps. They are definedbelow to be small when the parameters estimated fromthe synthetic data and those from the observations arecompatible. The azimuthal penalty coefficient pθ isdefined as,

ph ¼ wh½jhmaxobs −h

maxsyn j þ jhmin

obs −hminsyn j þ gh� ð5Þ

where θobsmax and θ obs

min are the maximum and minimumazimuths estimated from the observed seismogramsdescribed above, while θsyn

max and θ synmin are the maximum

and minimum azimuths for the synthetic seismograms.wθ and γθ are constants which are introduced in order to

Fig. 8. An example of the area of apparent tremor epicenters for the west array data, estimated for 10 min starting from 22:00, November 26, 1999 (thesame data as that of Figs. 6a and 7a). The number of long time windows whose source areas include each grid point is shown with gray scale. Theepicentral area is seen as a smudge south of the crater. Two solid lines show the maximum and minimum values of estimated azimuth of the west arrayfor the 10 min (See the second panel of Fig. 6a. Apparent azimuth takes maximum value of 37° at 519 s, and minimum value of 3° at 468 s).


normalize the minimum and maximum values of pθfrom 0 to 1, respectively. Because the estimatedazimuths are not much affected by the noise amplitudeR, we fix R to 0, so that pθ is a function of LNW, LSE, A,B1, and B2. In a similar way, the amplitude penaltycoefficient is defined as,

pa ¼ wa½jamaxobs −a

maxsyn j þ jamin

obs−aminsyn j þ ga� ð6Þ

where aobsmax and aobs

min represent the maximum andminimum RMS amplitudes of the observed seismo-grams of the center of the west array, while asyn

max andasynmin are those for the synthetic seismograms. wa and γa

are constants to normalize pa from 0 to 1. A similarpenalty coefficient is defined also for semblance as,

ps ¼ ws½jhŜiobs−hŜisynj þ gs� ð7Þ

where ⟨Ŝ⟩ is the averaged Ŝ over the entire data window.ws and γs represent constants which we introduce to

normalize the minimum and maximum value of ps from0 to 1. We calculate pa and ps fixing LNW=4 and LSE=3,anticipating that they do not depend much on the sourcelocations, so that these two coefficients are functions ofA, B1, B2, and R. We then obtain the penalty coefficient pby summing up these three coefficients as,

pðLNE; LSE;A;B1;B2;RÞ¼ phðLNE; LSE;A;B1;B2Þ þ paðA;B1;B2;RÞ

þ psðA;B1;B2;RÞ ð8Þ

Finally, for each pair of the source locations (LNW, LSE),we search the parameters of A, B1, B2, and R for which ptakes the minimum value for the ranges shown in theTable 1. Fig. 9b shows the minimum penalty coefficientas a function of LSE with LNW as a parameter. Each linein the figure corresponds to a different LNW. Theminimum p corresponding to the best fit to theobservations is obtained for LNW=7 and LSE=1. Forthis pair the estimated amplitudes are A=4, B1=2,

Fig. 9. (a) Locations of the imaginary sources used for the synthetic test to determine the two source locations. In the test, the source locations of theNWand SE sources are represented by the source number shown in this figure, and defined as LNW and LSE, respectively. (b) The minimum penaltycoefficient as a function of LNW with LSE as a parameter. Different lines correspond to the minimum penalty coefficients for different LSE. The penaltycoefficients take small values when we choose LSE smaller than 3, and LNW larger than 6. When we set LSE to 1, the penalty coefficient takes aminimum value for LNW=7.


Table 1The ranges of the model parameters of the synthetic test

LSE 0, 1, 2, 3, 4, 5LNW LSE+1, LSE+2,…, 10A 1, 2, 3, 4, 5, 6, 7, 8, 9B1 0, 1,…, 9–A, 10–AB2 10–A–B1

R 0, 1,…, 19, 20


B2=4, and R=6. Figs. 10 and 11 show the parameters atthe west array and the apparent epicentral areadetermined from the synthetic data, respectively.When we choose LNW slightly different from 7, LSEtends to be less than 2. Although the source locationsand amplitudes somewhat depend on the observation

Fig. 10. Estimated parameters for the synthetic data at the west array. Synth(LNW=7, LSE=1, A=4, B1=2, B2=4, R=6). Seismogram at station 00 (top), arow), and semblance coefficient (bottom row) are shown. The estimated paraRMS of the amplitude is superimposed with a line of light gray.

time window used making their estimates somewhatuncertainties, the SE source tends to be located morethan 400 m distant from the NW source. We thereforeconclude that the two sources are separated by morethan 400 m although the absolute locations of the twosources are less certain.

5. Discussion

5.1. Comparison with the tremor source for the 2001observation

About two years after the 1999 experiment, weinstalled a larger cross-shaped array near the main crater

etic parameters are chosen to make the penalty coefficient minimumzimuth (second row), apparent slowness in seconds per kilometer (thirdmeters are plotted by solid lines with error bounds. In each panel, the

Fig. 11. Apparent epicentral area determined from the synthetic data. Seismograms used are the same as that in Fig. 10. Two imaginary sources(LNW=7, LSE=1) are marked by triangles.


in July, 2001 (Fig. 1). Fig. 12 shows the results obtainedfrom the 2001 array data. Since this array has a muchlarger aperture, we could locate the tremor epicenter byusing only one array on the basis of an assumption ofcylindrical wave radiation from epicenters. The azimuthof the epicenter is estimated to be about 35–45°counterclockwise from east, and the epicentral distanceis around 400 m. The estimated apparent slowness is inthe range of 0.7–1.0 (s/km). We should mention that atthe time of the 2001 observation, the activity of the SEsource whose amplitudes modulated in 1999 has beendecayed. On the other hand the northwest source of the1999 data may be identical to the tremor source of the2001 data. This may infer that the NW source has asustained supply of heat or volcanic gas from below,while the supply to the SE source ceased sometime afterthe 1999 experiment. The stability of the heat or gassupply to a shallow tremor source from depth woulddepend on the state of conduits through which volcanicgas flows. Although our observations might have caughta change in the conduit state below the main crater at

Aso, we do not have enough information to discussextensively what controls temporal change in the supplyof volcanic gas at this stage.

5.2. The extent and the depth of the tremor source

We note here that a real tremor source should have afinite extent, and the epicenters we have located may beregarded as the centroid location of the seismic momentrelease. The real extent of each tremor source is difficultto estimate accurately. For example, although theepicentral area estimated for the 2001 data forms anarrow band-like area (Fig. 12), it may not necessarilymean that the source region actually is as such.

We cannot estimate the source depth directly fromthe estimated values of the apparent slowness becausethe observed signals could contain surface waves andbody waves. Mori (2000) showed that the earliest part ofthe isolated events (Type c) seismograms mostlyconsists of body waves whose apparent slowness isabout 0.2 s/km. They also determined the source depth

Fig. 12. An example of the area of the apparent tremor epicenters for the 2001 array data, estimated for 43 min from 22:00:00 on Jul. 22, 2001. Thenumber of long time windows whose source areas include each grid point is shown with gray scale. The sensor locations for the 2001 observation arealso plotted. Triangles show the locations of two imaginary point sources estimated for the 1999 data (see text).


of the isolated events at about 600 m. The apparentslowness values of the continuous tremor are muchlarger than that of the isolated events, so that we maysafely infer that the source depth of the continuoustremor is shallower than 600 m.

5.3. Cause of the amplitude modulation

The mechanism of the amplitude modulation is notnecessarily clear at this stage. Ohminato and Davide(1997) observed modulation of tremor amplitude atSatsuma-ioujima. The period of the modulation theyreport is 50 min, which is much longer than that of Aso.They infer that the continuous tremor is generated at avent which emits volcanic gas, and that the modulationreflects the fluctuation in the gas emission rate that iscaused by the convection of magma in the conduit. AtAso, juvenile magma seemed not to exist at theshallowest part of the volcano edifice during the periodof the two experiments, and no obvious changes

concomitant with the modulation was observed for thefumarole activity, so that any mechanism associatedwith periodic magma convection is unlikely. Hydro-thermal processes are more plausible for the mechanismthan magma processes.

Hydrothermal origin of volcanic tremor is alsosuggested for at Kilauea volcano by Almendros et al.(2001), although they do not report any modulation oftremor amplitude. They determine the source region oftremor at 200 m northeast of the Halemaumau pit crater.The tremor source has a size of about 0.6×1.0×0.5 kmand its depth is shallower than 200 m. There is a gapbetween the location of the epicenter region and thecenter of the crater, as is in the case of Aso.

An alternative idea of the cause of the modulationwould be the mechanism which drives a geyser. Kieffer(1984) points out the relations between the seismicityand the eruption cycle of Old Faithful Geyser inYellowstone National Park. A cycle of the geyser is asfollows: (1) an underground reservoir is filled with


water, (2) the temperature of the water rises and reachesto the boiling point, (3) the water/steam mixture isemitted out of the conduit until the reservoir is empty.According to this model, the interval of the eruptionsdepends on the size of the reservoir, water flow rate intothe reservoir, and the rate of the heat transfer. Theinterval of the cycle of the Old Faithful Geyser is a fewtens of minutes, which is again much longer than that ofAso (80 s).

The geyser model needs a large amount of the liquidwater which is enough to fill the hot reservoir. For theAso volcano the existence of a large amount of groundwater under the active crater has been suggested byprevious researchers. Hase et al., (2005) detected lowresistivity regions at the depths of about 200 m andabout 1000 m under the active crater by the Magneto-Telluric (MT) observations. Tanaka (1993) proposes theoccurrence of rapid heating/cooling about 200 m belowthe active crater lake during the 1989 eruptive activitybased on the observations of the temporal change in thelocal magnetic dipole, and attributes it to the interactionof groundwater and superheated vapor. These seem tosupport a geyser-type model for the mechanism of theamplitude modulation at Aso, but details of the model,especially regarding the mechanism of rapid dischargeof water from the underground reservoir, remainunclear.

Yamamoto et al. (1999) detected a crack-like conduitat a few hundred meters southwest of the active crater atAso. The best estimate of the upper edge of the crack isat the depth of 400 m below the crater lake. Thecontinuous tremor is possibly generated near thetransport paths of the volcanic gas and/or magmawhich connect the upper edge of the crack-like conduitand the conical-shaped vent just below the active crater.The source region of the continuous tremor may thusreflect the structure of the conduit system at theuppermost edifice of the Aso volcano.

6. Conclusions

We analyze the seismic array records of thecontinuous tremor observed in 1999 at Aso volcano,and accurately locate the epicenters of the tremor.The estimated azimuth of the epicenter often changeswith time being synchronized with the tremoramplitude. If we assume the presence of two pointsources with fixed locations, one of them is locatedat 300 m west of the center of the active crater (NWsource) and the other at 200 m south of the crater(SE source). The estimated location of the NWsource in 1999 is close to that in 2001, possibly

being identical. The cause of the amplitude modula-tion might be explained by a geyser-type mechanism.The source region of the continuous tremor mayrepresent the structure of the conduit system at theuppermost part of the Aso volcano.

Acknowledgements

We would like to thank all who participated in theobservations: M. Sako, T. Hashimoto, M. Nakabou, M.Kato, T. Ohminato, J. Oikawa, G. Helffrich, A. Okabe,T. Nakajima, and K. Iwamura. We could not completethis work without their help. Comments by the twoanonymous reviewers greatly improved this paper. Weare indebted to Y. Tanaka, H. Hase, and M. Utsugi (AsoVolcanological Laboratory) for valuable discussion. Wethank T. Tsutsui for his advice about the velocitystructure of the Aso volcano.

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